Active Contours without Edges for Vector-Valued Images

Active Contours without Edges for Vector-Valued Images

2000 | Tony F. Chan, B. Yezrielev Sandberg, and Luminita A. Vese
This paper proposes an active contour algorithm for object detection in vector-valued images, such as RGB or multispectral images. The model extends the scalar Chan–Vese algorithm to the vector-valued case. It minimizes a Mumford–Shah functional over the length of the contour, plus the sum of the fitting error over each component of the vector-valued image. The model can detect edges both with and without gradient. It is robust to noise and does not require a priori denoising. The model is applied to various examples, including cases where objects are undetectable in scalar representations, such as objects with missing parts in different channels or occluded objects. The model also detects objects in color images that are invisible in each channel or in intensity. The algorithm uses the level set method of Osher and Sethian to determine the boundary of detected objects. Experimental results show that the model can detect missing information in each channel and the complete object, even in the presence of noise or occlusion. The model is able to detect edges without gradient, which is particularly useful in cases where gradient-based methods fail. The algorithm is applied to various types of images, including multispectral, color, and textured images, and is shown to be effective in detecting contours in noisy environments. The model is robust and can automatically detect interior contours. The paper concludes that the proposed model has all the benefits of the C–V algorithm, including robustness even with noisy data and automatic detection of interior contours.This paper proposes an active contour algorithm for object detection in vector-valued images, such as RGB or multispectral images. The model extends the scalar Chan–Vese algorithm to the vector-valued case. It minimizes a Mumford–Shah functional over the length of the contour, plus the sum of the fitting error over each component of the vector-valued image. The model can detect edges both with and without gradient. It is robust to noise and does not require a priori denoising. The model is applied to various examples, including cases where objects are undetectable in scalar representations, such as objects with missing parts in different channels or occluded objects. The model also detects objects in color images that are invisible in each channel or in intensity. The algorithm uses the level set method of Osher and Sethian to determine the boundary of detected objects. Experimental results show that the model can detect missing information in each channel and the complete object, even in the presence of noise or occlusion. The model is able to detect edges without gradient, which is particularly useful in cases where gradient-based methods fail. The algorithm is applied to various types of images, including multispectral, color, and textured images, and is shown to be effective in detecting contours in noisy environments. The model is robust and can automatically detect interior contours. The paper concludes that the proposed model has all the benefits of the C–V algorithm, including robustness even with noisy data and automatic detection of interior contours.
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[slides and audio] Active Contours without Edges for Vector-Valued Images